A kalman filter in the presence of outliers

A Kalman Filtering algorithm which is robust to observational outliers is developed by assuming that the measurement error may come from either one of two Normal distributions, and that the transition between these distributions is governed by a Markov Chain. The resulting algorithm is very simple, and consists of two parallel Kalman Filters having different gains. The state estimate is obtained as a weighted average of the estimates from the two parallel filters, where the weights are the posterior probabilities that the current observation comes from either of the two distributions. The large improvements obtained by this Robust Kalman Filter in the presence of outliers is demonstrated with examples.